I was wondering how i would get the angle from a set of coordinates (x,y). I mean the inside angle that makes a triangle.
For example, the points would be (2,5),(3,4), and (5,1)?
I am trying to think of a general approach as I want to program it.
As a side note, I am actually programming a navigation app that shows a user a top down map and calculates a route for the user to follow. I am taking coordinates from the route and trying to figure out when to tell the user to turn right or left. I figured I just need to figure out the angle of the coordinate the user is near and if its concave or convex....
The standard way to do this is to use dot product. For any vectors $u,v \in \mathbb{R}^n$, the angle $\theta$ in between is given by $$ \cos\theta = \frac{u \cdot v}{\lVert u \rVert \lVert v \rVert} $$ where $\lVert u \rVert$ is the Euclidean length of $u$.
In your case, you can let $a = [2,5], b = [3,4], c = [5,1]$. Then $u$ and $v$ are given by $u = a - b, v = c - b$.